Membrane modeling of pull-in instability in MEMS sensors and actuators

The pull-in behavior of a conductive elastic membrane over a rigid ground electrode as a prototype of MEMS pressure sensors or MEMS microvalves is studied. Elastic membrane theory is used to describe the deformation of the membrane, which together with electric loading forms a nonlinear electromechanical coupling problem. A closed-form solution on the deflection of the membrane has been obtained, in which both equilibrium and non-equilibrium states are observed The transition from the equilibrium state to the non-equilibrium state is related to the stiction failure mode occurring in the operation of MEMS devices. Defined as the electric potential difference between the membrane and the electrode at which the snap-through of the membrane to the electrode occurs, the pull-in electric voltage is derived in a closed form. It is proportional to the square root of the tensile force created in the stretch of the membrane and inversely proportional to the length of the membrane.